Abstract
This paper deals with a-priori estimates for Dirichlet's problem for quasilinear elliptic equations $$a_{ij} (x,u, \triangledown u)u_{x_i x_j } = f(x,u, \triangledown u)$$ in the plane. We give an a-priori estimate for the C2+α-norms of all solutions under the following assumptions only: The principal part is uniformly elliptic, f has quadratical growth with respect to ∇u, aij and f are Holder-continuous and an a-priori estimate for sup|u| is known.
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